8/11/13 NPTEL :: Chemical Engineering - Process Control and Instrumentation

nptel.iitm.ac.in/courses/103103037/2 1/1

Process Modeling

A mathematical model of a process is a set of differential and algebraic equations whose solution yields the static

and dynamic behavior of the process. In other words, a mathematical model essentially describes the physical and

chemical phenomena of a process. Unarguably, performing experiments is the best way to gather information

(data) about a process. However, time, effort and cost associated with experimental approach of gathering

information may not be an easy option, especially for costly experiments. Mathematical model is a good

alternative in such situations. However, it should be noted that a model is never a perfect alternative to the real life

process. There is always a scope of error, however small it may be, between model and the process. Nevertheless,

a reliable modelling exercise needs to be adopted so that the process/model mismatch remains as small as

possible.

A mathematical model is useful for various purposes in the process industries. A trainee operator can learn the

process details with the help of a process model. The operator needs to learn know-hows of critical situation and

perform what-if analysis for the process. Such critical situation is never advisable “to be created” in the real-life

plant operation. Hence, simulation of process model serves the purpose in this case. In fact the simulation of

process model is carried out for design, safety analysis and controller synthesis of that process. Trial of the

controller on a process model prior to the actual plant application is mandatory.

II.1 State variables and equations

The state variables are a set of fundamental dependent quantities whose values describe the natural state of a

given process. The state equations are set of differential equations which describe the progression of the states

with time. The state variables are primarily the fundamental quantities of a process viz., mass, energy and

momentum, whereas the state equations are generated out of conservation principle involving these fundamental

quantities.

Let S be the fundamental quantity. The state equation can be written as:

(II.1)